周全系統參數下最大化廣義分頻多工系統之頻譜效率

Abstract

近年來，由於廣義分頻多工（generalized frequency division multiplexing, GFDM）系統具有低頻帶外輻射（out-of-band emission, OOBE）、低延遲、高頻譜效率（spectral efficiency）的特性，因此被推出來做為取代正交分頻多工（orthogonal frequency division multiplexing, OFDM）系統的候選人之一。然而，廣義分頻多工系統會因為具有非么正的傳輸矩陣（transmitter matrix）而造成雜訊放大（noise enhancement）和接收端在均方誤差（mean square error, MSE）以及符元錯誤率（symbol error rate, SER）上有性能下降的情形。因此，過去多項研究探討了廣義分頻多工系統在最小化頻帶外輻射並維持良好頻帶內性能的原型濾波器（prototype filter）設計最佳化演算法。不過，這些最佳化方法沒有把副載波（subcarrier）大小、副符碼（subsymbol）大小、頻譜資源分配方法、循環前綴（cyclic prefix, CP）長度納為設計參數，而這些參數會影響到廣義分頻多工系統的頻譜效率。此外，一個有彈性的取樣頻率（sample rate）也會影響系統的頻譜效率，但前人並未對此做過研究。

在本研究中，我們設計了一道綜合參數的最佳化問題，在符合性能限制的條件下最大化廣義分頻多工系統的頻譜效率。我們提出了多項演算法來解決這道混合整數規劃問題（mixed integer programming problem）。另外，我們還應用了一些方法使提出的演算法更有效率。模擬結果顯示，我們提出的設計方法能夠比前人的方法達到更高的頻譜效率。

In recent years, generalized frequency division multiplexing (GFDM) systems have been promoted as an alternative to orthogonal frequency division multiplexing (OFDM) systems due to their low out-of-band emission (OOBE), low latency, and high spectral efficiency. However, GFDM systems can suffer from noise enhancement and in-band performance degradation in receiver mean square error (MSE) and symbol error rate (SER) from having non-unitary transmitter matrices. Therefore, filter optimization algorithms for GFDM to minimize OOBE while maintaining good in-band performance had been studied in the past. Nevertheless, these optimization methods didn't take subcarrier and subsymbol sizes, spectral resource allocation method, and CP length as optimization variables, and these factors have impacts on GFDM systems' spectral efficiency. Furthermore, the effect of flexible sample rates has not yet been studied, which can also sway the systems' spectral efficiency.

In this research, a joint optimization problem to maximize spectral efficiency for GFDM systems under performance constraints is introduced. The proposed method is presented to solve this mixed integer programming problem by dissecting it into simpler problems, and heuristics specific to the problems were incorporated to make the proposed method more time-efficient. Simulation results show that the proposed method is able to achieve higher spectral efficiency for GFDM systems compared to existing GFDM optimization methods.